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|In this Sudoku we've looking at number 7 and labelled two chains A and B and settled on the plus and minus symbols. I have labelled them so that they match the rule. (Don't make a category mistake and think the rule applies just because you've assigned the lables!).
Now, the yellow cell marked A- does not share a unit with any of B cells. However, all three cells marked A+ can see a B+ or a B- in one or more shared units. Since the solution cannot be both B+ and B- but must be at least all of B+ or all of B- every cell in A+ must be false and number 7 can be removed from all A+ cells.
Multi-Colouring Type 1 eg 1: Load Example or : From the Start
|This second example is provided to illustrate the idea a bit further. A+ is again the victim and all the labels are the same as the first example. It also shows that the chains can be quite short.
Interestingly, although B can be a chain of just two cells A must be a longer chain. Otherwise we'd be in a situation where the Sudoku has two solutions or multi-colouring can be reduced to a Unique Rectangle.
Multi-Colouring Type 1 eg 2: Load Example or : From the Start
|This is a bit of a mouthful. What we're looking at are cells marked A+ which can see B+ cells but A- cells cannot see B- cells. A+ and B+ both can't be true since they share units in two cases. One or perhaps both of the units marked A- and B- must be true. All cells that can see an A- and a B- can't contain the candidate, in this example number 8. In R3C5 an 8 can see R2C4 AND R8C5. Similarly the 8 in R7C4 can see R2C4 and R8C5/R7C9.|
Multi-Colouring Type 2, Example 1: Load Example or : From the Start
|This smaller example might be more easy to understand. The labels are the same so that one A+ can see a B+. There is just one place where a 7 is at the overlap of an A- and a B-.|
Multi-Colouring Type 2 eg 2: Load Example or : From the Start